To determine which falling object results in the least kinetic energy when it collides with the ground, we can use the formula for kinetic energy (KE):
\[ KE = \frac{1}{2} m v^2 \]
where \( m \) is the mass in kilograms and \( v \) is the velocity in meters per second.
Now, let's calculate the kinetic energy for each of the options:
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10 grams of dirt falling at 2 m/s:
- Convert mass to kilograms: \( 10 \text{ g} = 0.01 \text{ kg} \)
- Calculate KE: \[ KE = \frac{1}{2} (0.01 \text{ kg})(2 \text{ m/s})^2 = \frac{1}{2} (0.01)(4) = 0.02 \text{ J} \]
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100 grams of dirt falling at 15 m/s:
- Convert mass to kilograms: \( 100 \text{ g} = 0.1 \text{ kg} \)
- Calculate KE: \[ KE = \frac{1}{2} (0.1 \text{ kg})(15 \text{ m/s})^2 = \frac{1}{2} (0.1)(225) = 11.25 \text{ J} \]
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10 grams of water falling at 1 m/s:
- Convert mass to kilograms: \( 10 \text{ g} = 0.01 \text{ kg} \)
- Calculate KE: \[ KE = \frac{1}{2} (0.01 \text{ kg})(1 \text{ m/s})^2 = \frac{1}{2} (0.01)(1) = 0.005 \text{ J} \]
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100 grams of water falling at 10 m/s:
- Convert mass to kilograms: \( 100 \text{ g} = 0.1 \text{ kg} \)
- Calculate KE: \[ KE = \frac{1}{2} (0.1 \text{ kg})(10 \text{ m/s})^2 = \frac{1}{2} (0.1)(100) = 5 \text{ J} \]
Now, let's summarize the kinetic energies calculated:
- 10 grams of dirt at 2 m/s: 0.02 J
- 100 grams of dirt at 15 m/s: 11.25 J
- 10 grams of water at 1 m/s: 0.005 J
- 100 grams of water at 10 m/s: 5 J
The object with the least kinetic energy when it collides with the ground is 10 grams of water falling at 1 m/s, with a kinetic energy of 0.005 J.
1 answer